# Calculating Heights on the Ferris Wheel

• urthatarget
In summary, the Ferris Wheel, invented by George Ferris in 1893, has a diameter of 250 feet and makes 1 revolution every 50 seconds. The height of a seat on the wheel can be represented by h(t) = 125sin (pi/25t - pi/2) + 125, where t is the time in seconds and the ride begins at t = 0. To find the time when an individual is exactly 125 feet above the ground during the first 50 seconds of the ride, solve the equation h(t) = 125. In order to find when an individual is exactly 250 feet above the ground during the first 100 seconds of the ride, solve the equation h
urthatarget
In 1893, George Ferris engineered the Ferris Wheel. It was 250 feet in diameter. If the wheel makes 1 revolution every 50 seconds, then

h(t) = 125sin (pi/25t - pi/2) + 125

represents the height (h), in feet, of a seat on the wheel as a function of time (t), where t is measured in seconds. The ride begins when t = 0.

a.) During the first 50 seconds of the ride, at what time (t) is an individual on the Ferris Wheel exactly 125 feet above the ground?

b.) During the first 100 seconds of the ride, at what time (t) is an individual on the Ferris Wheel exactly 250 feet above the ground?

c.) During the first 50 seconds of the ride, over what interval of time (t) is an individual on the Ferris Wheel more than 125 feet above the ground?

Can someone help me solve part A so I can do the rest by myself. Thank you very much!

Last edited:
urthatarget said:
a.) During the first 50 seconds of the ride, at what time (t) is an individual on the Ferris Wheel exactly 125 feet above the ground?

They are simply saying, during one revolution, when is h(t) = 125. Solve for t.

urthatarget said:
In 1893, George Ferris engineered the Ferris Wheel. It was 250 feet in diameter. If the wheel makes 1 revolution every 50 seconds, then

h(t) = 125sin (pi/25t - pi/2) + 125
You mean h(t)= 125 sin((pi/25)t- pi/2)+ 125

represents the height (h), in feet, of a seat on the wheel as a function of time (t), where t is measured in seconds. The ride begins when t = 0.

a.) During the first 50 seconds of the ride, at what time (t) is an individual on the Ferris Wheel exactly 125 feet above the ground?
Solve the equation h(t)= 125 sin((pi/25)t- pi/2)+ 125= 125. For what values of x is sin(x)= 0?

b.) During the first 100 seconds of the ride, at what time (t) is an individual on the Ferris Wheel exactly 250 feet above the ground?

c.) During the first 50 seconds of the ride, over what interval of time (t) is an individual on the Ferris Wheel more than 125 feet above the ground?

Can someone help me solve part A so I can do the rest by myself. Thank you very much!

## What is the physics behind a Ferris wheel?

A Ferris wheel operates on the principles of centripetal force and angular motion. As the wheel turns, the riders experience a constantly changing direction of motion, causing a centripetal force that keeps them moving in a circular path. This force is balanced by the outward force of gravity, creating a stable and safe ride.

## How is the speed of a Ferris wheel calculated?

The speed of a Ferris wheel is calculated using the formula v = rω, where v is the linear speed, r is the radius of the wheel, and ω is the angular speed. The angular speed can be calculated by dividing the angle of rotation by the time taken to complete one revolution.

## What factors affect the motion of a Ferris wheel?

The motion of a Ferris wheel is affected by several factors, including the radius of the wheel, the angular speed, and the weight of the riders. The shape of the wheel and the presence of any external forces, such as wind, can also affect the motion.

## How does a Ferris wheel maintain its balance?

A Ferris wheel maintains its balance through the use of a counterweight system. The weight of the riders is counteracted by a weight on the opposite side of the wheel, ensuring that the center of mass remains at the center of the wheel and that the wheel does not tip over.

## Is a Ferris wheel an example of uniform circular motion?

Yes, a Ferris wheel is an example of uniform circular motion, as the riders experience a constant speed and a constantly changing direction of motion. This type of motion occurs when an object moves in a circular path at a constant speed.

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